Response surface modelling in quantitative risk analysis for life safety in case of fire

Abstract

This paper proposes part of a framework for the development of a risk assessment methodology to quantify the life safety risk of building occupants in the context of fire safety design. An important aspect of quantitative risk analysis (QRA) concerns taking into account the variability of the design parameters. In QRA for life safety in case of fire, one of the key research challenges to take probability into account is the complexity of the different submodels. Another key aspect is the high computational time for performing a set of simulations. In order to tackle these problems, a response surface model (RSM) for sub-models, which support the global QRA method, is useful. In this paper, this is illustrated in particular for the modelling of smoke spread. More specifically, the focus is on the development of a method and a model for estimating the RSM using a Least Squares (LS) technique or the Polynomial Chaos Expansion (PCE) approach. Both methods were found to be suitable for the intended purpose, but PCE provides the best fitting response surface model based on the obtained data for the case at hand. The model is tested in a practical case study with Computational Fluid Dynamics (CFD) incorporating the Fire Dynamics Simulator (FDS) model.

Introduction

In prescriptive fire safety legislation it is often implicitly assumed that when all the rules of the regulation are applied, the fire safety level is acceptable [1], [2], [3]. However, architectural demands have become increasingly challenging during the last decades as advances in structural engineering as well as material sciences have made it possible to realize buildings with complex configurations, which cannot always be built in accordance with existing codes. Therefore, globally, more and more countries change their legislation regarding fire safety and proceed designing buildings in function of objectives. Possible formats are objective-based [2], performance-based [1], [4] or risk-informed [5], [6] design, where the implicit acceptable safety level assumption in prescriptive rules now becomes explicit by showing the verified safety level. Although the aforementioned approaches still show some shortcomings [6], there is a consensus that a holistic approach is necessary in which the building configuration, user, content, safety systems and procedures are analysed together.

Risk-based methods provide a way to evolve towards such a holistic approach. More specifically, quantitative risk assessment techniques provide an opportunity to determine the safety level in a representative measure. The advantage is that both the magnitude and likelihood of hazards versus safeguards can be determined [7]. One of the main objectives of risk-based probabilistic methods is to take into account uncertainties (in addition to the deterministic quantification of scenarios and consequences) in a quantitative risk analysis (QRA), whereas in deterministic performance based designs uncertainty is generally dealt with by using safety factors [8]. However, one of the key problems when taking probability into account is the complexity of the different submodels such as fire spread, smoke spread, evacuation, etc. [9]. Another problem is the high computational time for performing a series of simulations (e.g. using finite difference models) which makes it impossible to analyse a high number of scenarios (according to a random set of input parameters). In order to tackle these problems, the number of samples has to be reduced. Several sampling techniques exist, such as importance sampling, Latin Hypercube sampling, surrogate-modelling, etc. Here, a response surface model (RSM) [10] is suggested for different types of submodels in order to significantly reduce the computational time when evaluating a high number of samples.

The purpose of the RSM, or ‘surrogate’ model, is to create a response surface with only a few solver evaluations. The creation of the response surface makes it possible to generate a (linear) interpolation function by which for a new combination of input data, the output can be generated without evaluating a new sample [11]. As a result, a high number of input combinations can be analysed with hardly any additional computational effort, which is of large importance when performing limit state analysis in order to evaluate probabilities and – consecutively – risks. The focus is on the development of an appropriate methodology and a surrogate model is proposed. The main advantage of the method is an increase of computational speed, from 10-fold up to 100-fold compared to Monte Carlo sampling and Importance sampling, while retaining an error of similar magnitude [11].

In the next section, the basic concept of surrogate modelling is explained. Two methods are investigated: traditional Least Squares (LS) techniques and a Polynomial Chaos Expansion (PCE) technique. In the subsequent section, a case study is performed using both methods. In this paper, the focus is on the proof of concept of the methodology for the CFD model in the context of smoke spread, based on a comparison of the results (in terms of slice files) for CO concentrations.